A measure-theoretic characterization of the Henstock-Kurzweil integral revisited

Tuo-Yeong Lee

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1221-1231
  • ISSN: 0011-4642

Abstract

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In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is F σ δ regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral.

How to cite

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Lee, Tuo-Yeong. "A measure-theoretic characterization of the Henstock-Kurzweil integral revisited." Czechoslovak Mathematical Journal 58.4 (2008): 1221-1231. <http://eudml.org/doc/37898>.

@article{Lee2008,
abstract = {In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is $F_\{\sigma \delta \}$ regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral.},
author = {Lee, Tuo-Yeong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Henstock variational measure; Henstock-Kurzweil integral; Henstock variational measure; Henstock-Kurzweil integral},
language = {eng},
number = {4},
pages = {1221-1231},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A measure-theoretic characterization of the Henstock-Kurzweil integral revisited},
url = {http://eudml.org/doc/37898},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Lee, Tuo-Yeong
TI - A measure-theoretic characterization of the Henstock-Kurzweil integral revisited
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1221
EP - 1231
AB - In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is $F_{\sigma \delta }$ regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral.
LA - eng
KW - Henstock variational measure; Henstock-Kurzweil integral; Henstock variational measure; Henstock-Kurzweil integral
UR - http://eudml.org/doc/37898
ER -

References

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  1. Bongiorno, D., Piazza, L. Di, Skvortsov, V. A., 10.1007/s10587-006-0037-1, Czech. Math. J. 56 (2006), 559-578. (2006) Zbl1164.26316MR2291756DOI10.1007/s10587-006-0037-1
  2. Piazza, L. Di, 10.1023/A:1013705821657, Czech. Math. J. 51 (2001), 95-110. (2001) MR1814635DOI10.1023/A:1013705821657
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  4. Henstock, R., Muldowney, P., Skvortsov, V. A., 10.1112/S0024609306018819, Bull. London Math. Soc. 38 (2006), 795-803. (2006) Zbl1117.28010MR2268364DOI10.1112/S0024609306018819
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  6. Tuo-Yeong, Lee, A full descriptive definition of the Henstock-Kurzweil integral in the Euclidean space, Proc. London Math. Soc. 87 (2003), 677-700. (2003) MR2005879
  7. Tuo-Yeong, Lee, 10.1016/j.jmaa.2004.05.033, J. Math. Anal. Appl. 298 (2004), 677-692. (2004) MR2086983DOI10.1016/j.jmaa.2004.05.033
  8. Tuo-Yeong, Lee, 10.1017/S030500410500839X, Math. Proc. Cambridge Philos. Soc. 138 (2005), 487-492. (2005) MR2138575DOI10.1017/S030500410500839X
  9. Tuo-Yeong, Lee, 10.1216/rmjm/1181069626, Rocky Mountain J. Math 35 (2005), 1981-1997. (2005) MR2210644DOI10.1216/rmjm/1181069626
  10. Tuo-Yeong, Lee, 10.1007/s10587-005-0050-9, Czech. Math. J. 55 (2005), 625-637. (2005) MR2153087DOI10.1007/s10587-005-0050-9
  11. Tuo-Yeong, Lee, 10.1016/j.jmaa.2005.10.045, J. Math. Anal. Appl. 323 (2006), 741-745. (2006) MR2262241DOI10.1016/j.jmaa.2005.10.045
  12. Thomson, B. S., Derivates of interval functions, Mem. Amer. Math. Soc. 93 (1991). (1991) Zbl0734.26003MR1078198
  13. Ward, A. J., On the derivation of additive interval functions of intervals in m -dimensional space, Fund. Math. 28 (1937), 265-279. (1937) 

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